Eur. Phys. J. B (2013) 86: 235
https://doi.org/10.1140/epjb/e2013-40234-9

Regular Article

Electron-hole symmetry and solutions of Richardson pairing model

¹ Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerpen, Belgium
² Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Izhorskaya 13, 125412 Moscow, Russia

^a e-mail: Vyacheslav.Misko@ua.ac.be

Received: 18 December 2012
Received in final form: 20 March 2013
Published online: 29 May 2013

Abstract

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.